Conference ID: 970-024-45523
In this talk, I will discuss some orthogonality-free approaches for optimization problems on Stiefel manifold. Stiefel manifold consists of matrices with orthogonal columns. Optimization problems with orthogonality constraints appear in many important applications such as leading eigenvalues computation, discretized Kohn-Sham total energy minimization, and sparse principal component analysis. We present new algorithms for solving optimization problems on Stieful manifold. These algorithms are based on penalty functions, thus there are no needs to carry out orthogonalization calculations in each iteration. The major computation cost of orthogonality-free algorithms is in the form of matrix-matrix multiplication, which has the advantage of being parallelized easily. Problems with both smooth and nonsmooth objective functions are considered. Theoretical properties of our alrogithms are discussed and numerical experiments are also presented.
Ya-xiang Yuan, Professor at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences. He graduated from Xiangtan University in 1981, obtained Ph.D.from University of Cambridge - England in 1986.
Professor Yuan works on numerical methods for nonlinear optimization, he has made outstanding contributions to trust region algorithms, quasiNewton methods, nonlinear conjugate gradient methods and subspace methods. He was the Director of Institute of Computational Mathematics and Scientific/Engineering Computing of CAS(1995-2006). Director of State Key Laboratory of Scientific and Engineering Computing(1997-2005). Vice President of Academy of Math. and Systems Science of CAS(1998-2006). He won numerous awards, including Fox Prize(1985, London), Young Scientist Award of China(1996, Beijing). Second Prize of National Natural Science Award(2006, Beijing), S.S. Chern Award of Chinese Mathematical Society(2011),TWAS prize in Mathematics(2014), Su Buqing Prize of China SIAM (2016) and Ho-Leung-Ho-Lee Prize (2016). He gave a Plenary Lectures at the ICIAM 1999, and an invited lecture at the ICM-2014. He was elected as an academician of CAS in 2011. Fellow of SIAM (2011), Fellow of AMS (2012), Corresponding Member of Brazilian Academy of Science(2014), and Fellow of TWAS(2015).
Currently, he is pesident of The International Council for Industrial and Applied Mathematics, editor-in-chief of “Science China: Mathematics” and editor-in-chief of “Journal of the OR Society of China”.